Araştırma Makalesi
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Yıl 2023, Cilt: 16 Sayı: 1, 181 - 195, 30.04.2023

Zlatko Erjavec Jun-ichi Inoguchi

https://doi.org/10.36890/iejg.1243521

Öz

Anahtar Kelimeler

magnetic curve; Killing vector field; hyperbolic space

Kaynakça

  • [1] Anosov, D. V., Sinaĭ, Y. G.: Some smooth ergodic systems, Uspekhi Mat. Nauk. 22 (5), 107–172 (1967). English translation: Russ. Math. Surv. 22 (5), 103–167 (1967).
  • [2] Arnol’d, V. I.: Some remarks on flows of line elements and frames. Dokl. Akad. Nauk. SSSR. 138, 255–257 (1961). English translation: Sov. Math. Dokl. 2, 562–564 (1961).
  • [3] Arnol’d, V. I.: First steps in symplectic topology. Uspekhi Mat. Nauk. 41 (6), 3–18 (1986). English translation: Russ. Math. Surv. 41, 1–21 (1986).
  • [4] Druţă-Romaniuc, S. L., Inoguchi, J., Munteanu, M. I.: Killing slant magnetic curves in the 3-dimensional Heisenberg group Nil3. Int. J. Geom. Methods Mod. Phys., Online Ready 2350094 (2023), https://doi.org/10.1142/S0219887823500949.
  • [5] Druţă-Romaniuc, S. L., Inoguchi, J., Munteanu, M. I., Nistor, A. I.: Magnetic curves in Sasakian manifolds. J. Nonlinear Math. Phys. 22 (3), 428–447 (2015).
  • [6] Druţă-Romaniuc, S. L., Munteanu, M. I.: Magnetic curves corresponding to Killing magnetic fields in E3. J. Math. Phys. 52, 113506 (2011).
  • [7] Duggal, K. L.: Geometry developed by the electromagnetic tensor field. Ann. Mat. Pura Appl. 119 (4), 239–245 (1979).
  • [8] Duggal, K. L.: Einstein-Maxwell equations compatible with certain Killing vectors with light velocity. Ann. Mat. Pura Appl. 120 (4), 263–268 (1979).
  • [9] Duggal, K. L.: On the four-current source of the electromagnetic fields. Ann. Mat. Pura Appl. 120 (4), 305–313 (1979).
  • [10] Duggal, K. L.: On Einstein-Maxwell field equations. Tensor. 34 (2), 199–204 (1980).
  • [11] Duggal, K. L.: On the geometry of electromagnetic fields of second class. Indian J. Pure Appl. Math. 14 (4), 455–461 (1983).
  • [12] Erjavec, Z.: On Killing magnetic curves in Sl(2, R) geometry. Rep. Math. Phys. 84 (3), 333–350 (2019).
  • [13] Erjavec, Z., Inoguchi, J.: Killing magnetic curves in Sol space. Math. Phys. Anal. Geom. 21, Article number 15, (2018).
  • [14] Erjavec, Z., Inoguchi, J.: J-trajectories in 4-dimensional solvable Lie group Sol40. Math. Phys. Anal. Geom. 25, Article number 8, (2022).
  • [15] Erjavec, Z., Inoguchi, J.: J-trajectories in 4-dimensional solvable Lie group Sol41. submitted.
  • [16] Erjavec, Z., Klemenˇci´c, D., Bosak, M.: On Killing magnetic curves in hyperboloid model of SL(2, R) geometry. Sarajevo J. Math., to appear.
  • [17] Ginzburg, V. L.: A charge in a magnetic field: Arnold’s problems 1981-9, 1982-24, 1984-4, 1994-14, 1994-35, 1996-17,1996-18, in Arnold’s problems (V.I. Arnold ed.) Springer-Verlag and Phasis, 395–401 (2004).
  • [18] Ikawa, O.: Motion of charged particles in homogeneous Kähler and homogeneous Sasakian manifolds. Far East J. Math. Sci. 14 (3), 283–302 (2004).
  • [19] Inoguchi, J., Munteanu, M. I.: Periodic magnetic curves in Berger spheres. Tohoku Math. J. 69 (1), 113–128 (2017).
  • [20] Inoguchi, J., Munteanu, M. I.: Magnetic curves in the real special linear group. Adv. Theor. Math. Phys. 23 (8), 2161–2205 (2019).
  • [21] Inoguchi, J., Munteanu, M. I.: Slant curves and magnetic curves. In: Contact geometry of slant submanifolds, Springer, Singapore, 199–259 (2022).
  • [22] Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry. Vol II. Interscience Publishers. (1969).
  • [23] Kowalski, O., Vanhecke, L., Riemannian manifolds with homogeneous geodesics. Boll. Un. Mat. Ital. B 5 (7), 189–246 (1991).
  • [24] Munteanu, M. I., Nistor, A. I.: The classification of Killing magnetic curves in S2 × R. J. Geom. Phys. 62 (2), 170–182 (2012).
  • [25] Nistor, A. I.: Motion of charged particles in a Killing magnetic field in H2 × R. Rend. Sem. Mat. Univ. Politec. Torino. 73/1 (3-4), 161–170 (2016).
  • [26] O’Neill, B.: Semi-Riemannian Geometry with Applications to Relativity. Academic Press. London. (1983).
  • [27] Scott, P.: The geometries of 3-manifolds. Bull. London Math. Soc. 15, 401-487 (1983).
  • [28] Thurston, W. M.: Three-dimensional Geometry and Topology I. Princeton Math. Series. 35, (1997).

Killing Magnetic Curves in $\: \mathbb{H}^{3}$

Yıl 2023, Cilt: 16 Sayı: 1, 181 - 195, 30.04.2023

Zlatko Erjavec Jun-ichi Inoguchi

https://doi.org/10.36890/iejg.1243521

Öz

We consider magnetic curves corresponding to the Killing magnetic fields in hyperbolic 3-space.

Anahtar Kelimeler

Magnetic curve Killing vector field hyperbolic space

Kaynakça

  • [1] Anosov, D. V., Sinaĭ, Y. G.: Some smooth ergodic systems, Uspekhi Mat. Nauk. 22 (5), 107–172 (1967). English translation: Russ. Math. Surv. 22 (5), 103–167 (1967).
  • [2] Arnol’d, V. I.: Some remarks on flows of line elements and frames. Dokl. Akad. Nauk. SSSR. 138, 255–257 (1961). English translation: Sov. Math. Dokl. 2, 562–564 (1961).
  • [3] Arnol’d, V. I.: First steps in symplectic topology. Uspekhi Mat. Nauk. 41 (6), 3–18 (1986). English translation: Russ. Math. Surv. 41, 1–21 (1986).
  • [4] Druţă-Romaniuc, S. L., Inoguchi, J., Munteanu, M. I.: Killing slant magnetic curves in the 3-dimensional Heisenberg group Nil3. Int. J. Geom. Methods Mod. Phys., Online Ready 2350094 (2023), https://doi.org/10.1142/S0219887823500949.
  • [5] Druţă-Romaniuc, S. L., Inoguchi, J., Munteanu, M. I., Nistor, A. I.: Magnetic curves in Sasakian manifolds. J. Nonlinear Math. Phys. 22 (3), 428–447 (2015).
  • [6] Druţă-Romaniuc, S. L., Munteanu, M. I.: Magnetic curves corresponding to Killing magnetic fields in E3. J. Math. Phys. 52, 113506 (2011).
  • [7] Duggal, K. L.: Geometry developed by the electromagnetic tensor field. Ann. Mat. Pura Appl. 119 (4), 239–245 (1979).
  • [8] Duggal, K. L.: Einstein-Maxwell equations compatible with certain Killing vectors with light velocity. Ann. Mat. Pura Appl. 120 (4), 263–268 (1979).
  • [9] Duggal, K. L.: On the four-current source of the electromagnetic fields. Ann. Mat. Pura Appl. 120 (4), 305–313 (1979).
  • [10] Duggal, K. L.: On Einstein-Maxwell field equations. Tensor. 34 (2), 199–204 (1980).
  • [11] Duggal, K. L.: On the geometry of electromagnetic fields of second class. Indian J. Pure Appl. Math. 14 (4), 455–461 (1983).
  • [12] Erjavec, Z.: On Killing magnetic curves in Sl(2, R) geometry. Rep. Math. Phys. 84 (3), 333–350 (2019).
  • [13] Erjavec, Z., Inoguchi, J.: Killing magnetic curves in Sol space. Math. Phys. Anal. Geom. 21, Article number 15, (2018).
  • [14] Erjavec, Z., Inoguchi, J.: J-trajectories in 4-dimensional solvable Lie group Sol40. Math. Phys. Anal. Geom. 25, Article number 8, (2022).
  • [15] Erjavec, Z., Inoguchi, J.: J-trajectories in 4-dimensional solvable Lie group Sol41. submitted.
  • [16] Erjavec, Z., Klemenˇci´c, D., Bosak, M.: On Killing magnetic curves in hyperboloid model of SL(2, R) geometry. Sarajevo J. Math., to appear.
  • [17] Ginzburg, V. L.: A charge in a magnetic field: Arnold’s problems 1981-9, 1982-24, 1984-4, 1994-14, 1994-35, 1996-17,1996-18, in Arnold’s problems (V.I. Arnold ed.) Springer-Verlag and Phasis, 395–401 (2004).
  • [18] Ikawa, O.: Motion of charged particles in homogeneous Kähler and homogeneous Sasakian manifolds. Far East J. Math. Sci. 14 (3), 283–302 (2004).
  • [19] Inoguchi, J., Munteanu, M. I.: Periodic magnetic curves in Berger spheres. Tohoku Math. J. 69 (1), 113–128 (2017).
  • [20] Inoguchi, J., Munteanu, M. I.: Magnetic curves in the real special linear group. Adv. Theor. Math. Phys. 23 (8), 2161–2205 (2019).
  • [21] Inoguchi, J., Munteanu, M. I.: Slant curves and magnetic curves. In: Contact geometry of slant submanifolds, Springer, Singapore, 199–259 (2022).
  • [22] Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry. Vol II. Interscience Publishers. (1969).
  • [23] Kowalski, O., Vanhecke, L., Riemannian manifolds with homogeneous geodesics. Boll. Un. Mat. Ital. B 5 (7), 189–246 (1991).
  • [24] Munteanu, M. I., Nistor, A. I.: The classification of Killing magnetic curves in S2 × R. J. Geom. Phys. 62 (2), 170–182 (2012).
  • [25] Nistor, A. I.: Motion of charged particles in a Killing magnetic field in H2 × R. Rend. Sem. Mat. Univ. Politec. Torino. 73/1 (3-4), 161–170 (2016).
  • [26] O’Neill, B.: Semi-Riemannian Geometry with Applications to Relativity. Academic Press. London. (1983).
  • [27] Scott, P.: The geometries of 3-manifolds. Bull. London Math. Soc. 15, 401-487 (1983).
  • [28] Thurston, W. M.: Three-dimensional Geometry and Topology I. Princeton Math. Series. 35, (1997).
Toplam 28 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Zlatko Erjavec 0000-0002-9402-1069

Jun-ichi Inoguchi 0000-0002-6584-5739

Yayımlanma Tarihi 30 Nisan 2023
Kabul Tarihi 8 Nisan 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 16 Sayı: 1

Kaynak Göster

APA Erjavec, Z., & Inoguchi, J.-i. (2023). Killing Magnetic Curves in $\: \mathbb{H}^{3}$. International Electronic Journal of Geometry, 16(1), 181-195. https://doi.org/10.36890/iejg.1243521
AMA Erjavec Z, Inoguchi Ji. Killing Magnetic Curves in $\: \mathbb{H}^{3}$. Int. Electron. J. Geom. Nisan 2023;16(1):181-195. doi:10.36890/iejg.1243521
Chicago Erjavec, Zlatko, ve Jun-ichi Inoguchi. “Killing Magnetic Curves in $\: \mathbb{H}^{3}$”. International Electronic Journal of Geometry 16, sy. 1 (Nisan 2023): 181-95. https://doi.org/10.36890/iejg.1243521.
EndNote Erjavec Z, Inoguchi J-i (01 Nisan 2023) Killing Magnetic Curves in $\: \mathbb{H}^{3}$. International Electronic Journal of Geometry 16 1 181–195.
IEEE Z. Erjavec ve J.-i. Inoguchi, “Killing Magnetic Curves in $\: \mathbb{H}^{3}$”, Int. Electron. J. Geom., c. 16, sy. 1, ss. 181–195, 2023, doi: 10.36890/iejg.1243521.
ISNAD Erjavec, Zlatko - Inoguchi, Jun-ichi. “Killing Magnetic Curves in $\: \mathbb{H}^{3}$”. International Electronic Journal of Geometry 16/1 (Nisan 2023), 181-195. https://doi.org/10.36890/iejg.1243521.
JAMA Erjavec Z, Inoguchi J-i. Killing Magnetic Curves in $\: \mathbb{H}^{3}$. Int. Electron. J. Geom. 2023;16:181–195.
MLA Erjavec, Zlatko ve Jun-ichi Inoguchi. “Killing Magnetic Curves in $\: \mathbb{H}^{3}$”. International Electronic Journal of Geometry, c. 16, sy. 1, 2023, ss. 181-95, doi:10.36890/iejg.1243521.
Vancouver Erjavec Z, Inoguchi J-i. Killing Magnetic Curves in $\: \mathbb{H}^{3}$. Int. Electron. J. Geom. 2023;16(1):181-95.
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